00. Distance and Displacement
Motion in One Dimensions

141366 A boy on a cycle pedals around a circle of 20 meters radius at a speed of \(20 \mathrm{~m} / \mathrm{s}\). The combined mass of the body and the cycle makes angle \(\theta\) with the vertical so that it may not fall. The value of \(\theta\) is \(\left(g=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)\)

1 \(60.25^{\circ}\)
2 63.90
3 26.12
4 \(30.00^{\circ}\)
Motion in One Dimensions

141367 A police party is moving in jeep at a constant' speed \(V\), They saw a thief at a distance \(z\) on a motorcycle which is at rest. The moment the police saw the thief, the thief started at constant acceleration a which of the following relations is true if the police is able to catch the thief?

1 \(\mathrm{V}^{2} \lt \mathrm{ax}\)
2 \(\mathrm{V}^{2} \lt 2 \mathrm{ax}\)
3 \(\mathrm{V}^{2} \geq 2 \mathrm{ax}\)
4 \(\mathrm{V}^{2}=\mathrm{ax}\)
Motion in One Dimensions

141368 A car moves from \(X\) to \(Y\) with a uniform speed \(v_{u}\) and returns to \(Y\) with a uniform speed \(v_{d}\). The average speed for this round trip is

1 \(\frac{2 v_{d} v_{u}}{v_{d}+v_{u}}\)
2 \(\sqrt{v_{d}+v_{d}}\)
3 \(\frac{v_{d} v_{u}}{v_{d}+v_{u}}\)
4 \(\frac{v_{d}+v_{u}}{2}\)
Motion in One Dimensions

141369 A car starts from rest, moves with an acceleration \(a\) and then decelerates at a constant rate \(b\) for sometimes to come to rest. If the total time taken is \(t\). The maximum velocity of car is given by:

1 \(\frac{a b t}{(a+b)}\)
2 \(\frac{a^{2} t}{a+b}\)
3 \(\frac{a t}{(a+b)}\)
4 \(\frac{b^{2} t}{a+b}\)
Motion in One Dimensions

141370 A police jeep is chasing with velocity of 45 \(\mathrm{km} / \mathrm{h}\). A thief in another jeep moving with velocity \(153 \mathrm{~km} / \mathrm{h}\). Police fires a bullet with muzzle velocity of \(180 \mathrm{~m} / \mathrm{s}\). The velocity it will strike the car the thief is

1 \(150 \mathrm{~m} / \mathrm{s}\)
2 \(27 \mathrm{~m} / \mathrm{s}\)
3 \(450 \mathrm{~m} / \mathrm{s}\)
4 \(250 \mathrm{~m} / \mathrm{s}\)
Motion in One Dimensions

141366 A boy on a cycle pedals around a circle of 20 meters radius at a speed of \(20 \mathrm{~m} / \mathrm{s}\). The combined mass of the body and the cycle makes angle \(\theta\) with the vertical so that it may not fall. The value of \(\theta\) is \(\left(g=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)\)

1 \(60.25^{\circ}\)
2 63.90
3 26.12
4 \(30.00^{\circ}\)
Motion in One Dimensions

141367 A police party is moving in jeep at a constant' speed \(V\), They saw a thief at a distance \(z\) on a motorcycle which is at rest. The moment the police saw the thief, the thief started at constant acceleration a which of the following relations is true if the police is able to catch the thief?

1 \(\mathrm{V}^{2} \lt \mathrm{ax}\)
2 \(\mathrm{V}^{2} \lt 2 \mathrm{ax}\)
3 \(\mathrm{V}^{2} \geq 2 \mathrm{ax}\)
4 \(\mathrm{V}^{2}=\mathrm{ax}\)
Motion in One Dimensions

141368 A car moves from \(X\) to \(Y\) with a uniform speed \(v_{u}\) and returns to \(Y\) with a uniform speed \(v_{d}\). The average speed for this round trip is

1 \(\frac{2 v_{d} v_{u}}{v_{d}+v_{u}}\)
2 \(\sqrt{v_{d}+v_{d}}\)
3 \(\frac{v_{d} v_{u}}{v_{d}+v_{u}}\)
4 \(\frac{v_{d}+v_{u}}{2}\)
Motion in One Dimensions

141369 A car starts from rest, moves with an acceleration \(a\) and then decelerates at a constant rate \(b\) for sometimes to come to rest. If the total time taken is \(t\). The maximum velocity of car is given by:

1 \(\frac{a b t}{(a+b)}\)
2 \(\frac{a^{2} t}{a+b}\)
3 \(\frac{a t}{(a+b)}\)
4 \(\frac{b^{2} t}{a+b}\)
Motion in One Dimensions

141370 A police jeep is chasing with velocity of 45 \(\mathrm{km} / \mathrm{h}\). A thief in another jeep moving with velocity \(153 \mathrm{~km} / \mathrm{h}\). Police fires a bullet with muzzle velocity of \(180 \mathrm{~m} / \mathrm{s}\). The velocity it will strike the car the thief is

1 \(150 \mathrm{~m} / \mathrm{s}\)
2 \(27 \mathrm{~m} / \mathrm{s}\)
3 \(450 \mathrm{~m} / \mathrm{s}\)
4 \(250 \mathrm{~m} / \mathrm{s}\)
Motion in One Dimensions

141366 A boy on a cycle pedals around a circle of 20 meters radius at a speed of \(20 \mathrm{~m} / \mathrm{s}\). The combined mass of the body and the cycle makes angle \(\theta\) with the vertical so that it may not fall. The value of \(\theta\) is \(\left(g=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)\)

1 \(60.25^{\circ}\)
2 63.90
3 26.12
4 \(30.00^{\circ}\)
Motion in One Dimensions

141367 A police party is moving in jeep at a constant' speed \(V\), They saw a thief at a distance \(z\) on a motorcycle which is at rest. The moment the police saw the thief, the thief started at constant acceleration a which of the following relations is true if the police is able to catch the thief?

1 \(\mathrm{V}^{2} \lt \mathrm{ax}\)
2 \(\mathrm{V}^{2} \lt 2 \mathrm{ax}\)
3 \(\mathrm{V}^{2} \geq 2 \mathrm{ax}\)
4 \(\mathrm{V}^{2}=\mathrm{ax}\)
Motion in One Dimensions

141368 A car moves from \(X\) to \(Y\) with a uniform speed \(v_{u}\) and returns to \(Y\) with a uniform speed \(v_{d}\). The average speed for this round trip is

1 \(\frac{2 v_{d} v_{u}}{v_{d}+v_{u}}\)
2 \(\sqrt{v_{d}+v_{d}}\)
3 \(\frac{v_{d} v_{u}}{v_{d}+v_{u}}\)
4 \(\frac{v_{d}+v_{u}}{2}\)
Motion in One Dimensions

141369 A car starts from rest, moves with an acceleration \(a\) and then decelerates at a constant rate \(b\) for sometimes to come to rest. If the total time taken is \(t\). The maximum velocity of car is given by:

1 \(\frac{a b t}{(a+b)}\)
2 \(\frac{a^{2} t}{a+b}\)
3 \(\frac{a t}{(a+b)}\)
4 \(\frac{b^{2} t}{a+b}\)
Motion in One Dimensions

141370 A police jeep is chasing with velocity of 45 \(\mathrm{km} / \mathrm{h}\). A thief in another jeep moving with velocity \(153 \mathrm{~km} / \mathrm{h}\). Police fires a bullet with muzzle velocity of \(180 \mathrm{~m} / \mathrm{s}\). The velocity it will strike the car the thief is

1 \(150 \mathrm{~m} / \mathrm{s}\)
2 \(27 \mathrm{~m} / \mathrm{s}\)
3 \(450 \mathrm{~m} / \mathrm{s}\)
4 \(250 \mathrm{~m} / \mathrm{s}\)
Motion in One Dimensions

141366 A boy on a cycle pedals around a circle of 20 meters radius at a speed of \(20 \mathrm{~m} / \mathrm{s}\). The combined mass of the body and the cycle makes angle \(\theta\) with the vertical so that it may not fall. The value of \(\theta\) is \(\left(g=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)\)

1 \(60.25^{\circ}\)
2 63.90
3 26.12
4 \(30.00^{\circ}\)
Motion in One Dimensions

141367 A police party is moving in jeep at a constant' speed \(V\), They saw a thief at a distance \(z\) on a motorcycle which is at rest. The moment the police saw the thief, the thief started at constant acceleration a which of the following relations is true if the police is able to catch the thief?

1 \(\mathrm{V}^{2} \lt \mathrm{ax}\)
2 \(\mathrm{V}^{2} \lt 2 \mathrm{ax}\)
3 \(\mathrm{V}^{2} \geq 2 \mathrm{ax}\)
4 \(\mathrm{V}^{2}=\mathrm{ax}\)
Motion in One Dimensions

141368 A car moves from \(X\) to \(Y\) with a uniform speed \(v_{u}\) and returns to \(Y\) with a uniform speed \(v_{d}\). The average speed for this round trip is

1 \(\frac{2 v_{d} v_{u}}{v_{d}+v_{u}}\)
2 \(\sqrt{v_{d}+v_{d}}\)
3 \(\frac{v_{d} v_{u}}{v_{d}+v_{u}}\)
4 \(\frac{v_{d}+v_{u}}{2}\)
Motion in One Dimensions

141369 A car starts from rest, moves with an acceleration \(a\) and then decelerates at a constant rate \(b\) for sometimes to come to rest. If the total time taken is \(t\). The maximum velocity of car is given by:

1 \(\frac{a b t}{(a+b)}\)
2 \(\frac{a^{2} t}{a+b}\)
3 \(\frac{a t}{(a+b)}\)
4 \(\frac{b^{2} t}{a+b}\)
Motion in One Dimensions

141370 A police jeep is chasing with velocity of 45 \(\mathrm{km} / \mathrm{h}\). A thief in another jeep moving with velocity \(153 \mathrm{~km} / \mathrm{h}\). Police fires a bullet with muzzle velocity of \(180 \mathrm{~m} / \mathrm{s}\). The velocity it will strike the car the thief is

1 \(150 \mathrm{~m} / \mathrm{s}\)
2 \(27 \mathrm{~m} / \mathrm{s}\)
3 \(450 \mathrm{~m} / \mathrm{s}\)
4 \(250 \mathrm{~m} / \mathrm{s}\)
Motion in One Dimensions

141366 A boy on a cycle pedals around a circle of 20 meters radius at a speed of \(20 \mathrm{~m} / \mathrm{s}\). The combined mass of the body and the cycle makes angle \(\theta\) with the vertical so that it may not fall. The value of \(\theta\) is \(\left(g=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)\)

1 \(60.25^{\circ}\)
2 63.90
3 26.12
4 \(30.00^{\circ}\)
Motion in One Dimensions

141367 A police party is moving in jeep at a constant' speed \(V\), They saw a thief at a distance \(z\) on a motorcycle which is at rest. The moment the police saw the thief, the thief started at constant acceleration a which of the following relations is true if the police is able to catch the thief?

1 \(\mathrm{V}^{2} \lt \mathrm{ax}\)
2 \(\mathrm{V}^{2} \lt 2 \mathrm{ax}\)
3 \(\mathrm{V}^{2} \geq 2 \mathrm{ax}\)
4 \(\mathrm{V}^{2}=\mathrm{ax}\)
Motion in One Dimensions

141368 A car moves from \(X\) to \(Y\) with a uniform speed \(v_{u}\) and returns to \(Y\) with a uniform speed \(v_{d}\). The average speed for this round trip is

1 \(\frac{2 v_{d} v_{u}}{v_{d}+v_{u}}\)
2 \(\sqrt{v_{d}+v_{d}}\)
3 \(\frac{v_{d} v_{u}}{v_{d}+v_{u}}\)
4 \(\frac{v_{d}+v_{u}}{2}\)
Motion in One Dimensions

141369 A car starts from rest, moves with an acceleration \(a\) and then decelerates at a constant rate \(b\) for sometimes to come to rest. If the total time taken is \(t\). The maximum velocity of car is given by:

1 \(\frac{a b t}{(a+b)}\)
2 \(\frac{a^{2} t}{a+b}\)
3 \(\frac{a t}{(a+b)}\)
4 \(\frac{b^{2} t}{a+b}\)
Motion in One Dimensions

141370 A police jeep is chasing with velocity of 45 \(\mathrm{km} / \mathrm{h}\). A thief in another jeep moving with velocity \(153 \mathrm{~km} / \mathrm{h}\). Police fires a bullet with muzzle velocity of \(180 \mathrm{~m} / \mathrm{s}\). The velocity it will strike the car the thief is

1 \(150 \mathrm{~m} / \mathrm{s}\)
2 \(27 \mathrm{~m} / \mathrm{s}\)
3 \(450 \mathrm{~m} / \mathrm{s}\)
4 \(250 \mathrm{~m} / \mathrm{s}\)